Season 1, episode 18.
Original air date: 17 July 1956.
A shady businessman collapses on an oceanside jetty, the apparent victim of a heart attack, but a vacationing March discovers blood and a needle near the body.
Cast: Boris Karloff (Col. Perceval March), Ewan Roberts (Inspector Ames), Robert Brown (Dr. Robert Hastings), Patricia Marmont (Marion Williams), Lloyd Lamble (Norman Kane), Adrienne Corri (Clara) and Richard O`Sullivan (Roger).
From IMDB,

The boy in this episode is played by Richard O'Sullivan - known to many as Robin Tripp in "Man About The House"

Most of "shadows_girl" review seems to be plagiarized from from this url:
http://www.mysterylist.com/lockedrm.htm
It's fairly sad and hypocritical that she didn't attribute a link to someone else's work, don't you think?

was the brainchild of famed detective story author John Dickson Carr (who also wrote under the name of "Carter Dickson". In the Golden Age of Detective Fiction he was considered the master of the "Locked Room Mystery".
In this genre he gave detective fiction TWO superstars of the art of deduction:
Dr. Gideon Fell who appears in such novels as HAG'S NOOK, THE BLIND BARBER, THE CASE OF THE CONSTANT SUICIDES and THE THREE COFFINS (among others) and Sir Henry Merrivale (also known as "The Old Man" who appears in novels like THE JUDAS WINDOW, THE SKELETON IN THE CLOCK, THE CURSE OF THE BRONZE LAMP and many more. Colonel March and his Department of Queer Complaints were relegated to short stories and this admirable tv series starring Boris Karloff.